When I do a bunch of guitar playing, my right (picking hand) shoulder is killing me for weeks. What hurts you?
The muscles in my left (chording) hand. Especially if I’ve been playing 12-string.
If your shoulder hurts from strumming, are you perhaps using your whole arm to strum? You should be using mostly your wrist, with your hand going backand forth but your arm relatively still. This might be your problem. Was I close?
My fret hand hurts too when I play. I’ve been spending a long time trying to get G minor down, and that always hurts the muscles and wrist of that hand.
When I played every day, I’d have some pain in my fretting fingertips where they touch the strings, but that’s it. I’ve never had any kind of lingering muscular pain (knock on wood).
Now I’m so busy (in law school) that I literally haven’t picked up a guitar in over six months. My fingertips are soft, and have no callus at all. I know it’s going to hurt like hell when I start playing again.
For me, it’s just my fingertips on the fret hand, because I don’t play as often as I used to, so the callouses that had built up years ago are now gone.
Nothing should hurt when you are playing or afterwards. Well, there will be some soreness while your hands/arms/fingers get strengthened up but this should not last past a month or two.
If your shoulder hurts after playing I would suspect that you are not holding the guitar in a good position. One thing I have noticed from people I have taught is that beginners tend to cramp themselves into weird positions when holding the guitar. Bad body position will cause pain and make it harder to play. Once learned bad body position is hard to fix.
Of coarse there are exceptions, like when I play standing up with my Les Paul my LEFT shoulder starts killing me after an hour or so because the thing weighs so damned much. A thicker strap didn’t do all that much…
Slee
I can hardly be considered a beginner. :):)
How would I know if I’m in a “bad” position?
By your sore shoulder. 
Seriously, look to see if you’re holding tension there. Unless you’re doing Pete Townshend-style windmill strokes, your shoulder shouldn’t move much at all. And unless you’re tensing it, it shouldn’t hurt. Try a different posture and see if that helps.
I don’t think I’m a beginner either, but when at time when I play for a while, my left shoulder (I’m right handed so this is my fretting side) gets super tense and starts to ache. I get this when I’m studying or typing on my computer so I think this is probably unrelated to guitar.
Some of my songs have a lot of barre chords; when I play those, I get a little claw-handed. I’m beginning to suspect I’m getting arthritic…I need some of Granny’s Rhumatiz’ Medicine… 
Oh, man. No lingering pains, but playing power chords just KILLS my left hand. It aches so much. I haven’t been able to make any sense of it - barre chords are fine, but three-string power chords hurt a lot.
Other than that, my fingertips sometimes get a little sore and tender if I’ve been playing a lot, but that’s pretty much it.
I agree with all the posters who state that a sore shoulder indicates something either larger than guitar or simply poor technique that needs adjusting.
I’ve played darn near 30 years and never suffered any discomfort except my fretting fingertips. Sure, when I play heavy barre-chorded songs I used to get “claw hand” as An Arky described it, but that’s about it. Now, when I am playing Keith Richards’-style bluesy chorded leads (don’t know how else to describe them - I am playing lead lines, but doing so using bends within partial chords up the neck - typically in Open G or a variant I use), then I get a little claw-handed, but that’s it.
Slee - how heavy is your Les Paul? I have two - one is 9lbs and the other 9.3. Both are okay to play for several hours - I use a Franklin strap on each, which is wide but not padded - just supple, high-quality leather…
This one’s easy. My left wrist (neck side). Don’t know why… it feels like I’m bending my hand like crazy, but there’s really no other way to hold the guitar.
As for what I play, I play mostly ska chords in my band, so just lots of barre-mute-barre-mute, really really fast, over and over and over, changing chords 2 times every measure or so.
Jeepers, it looks like it’s only me. I need a guitar-savvy chiro or yoga instructor or something.
Your wallet.
Strummin’ don’t pay beans.
I don’t know how much my Paul weighs, don’t have a scale in the house so I can’t check. It’s fairly heavy, ~10 lbs I’d guess, same as yours. I bought a wider strap but apparently it isn’t wide enough. I usually play sitting down so getting a new strap never crosses my mind when I am at the music store.
NoCoolUserName, as I said in my first post, if you learn bad body position when your first start playing it is hard to stop. My guess would be that, if you play sitting down, you probably hold the guitar on your right leg. If you do that it can cause you to scrunch up your right shoulder so that your pick hand is in the correct position. Scrunching up your shoulder would cause it to be sore because our are holding it in an unnatural position. Try putting the guitar on your left leg like this guy. It’ll probably take a bit to get used to but it should help your shoulder. Once you get used to the position, it’ll probably take a couple weeks, you should notice that you want to hold the guitar differently when you stand up.
EvilHamsterOnCrack, if your left wrist hurts I can almost guarantee that your elbow isn’t out far enough from your body. If you pull your elbow in it twists your wrist and that puts a lot of strain on it. Pop your elbow out away from your body. If it is hard to keep out at first stick a pillow between your arm and side. Your hand and arm should be at a right angle to the neck in a pretty straight line. You don’t want much lateral bend in your wrist. The only way to do that is have your elbow away from your body.
Hope this helps.
Slee
D’oh, sorry about the bold. I apparently missed a closing tag. That’s what I get for posting after work
Slee